Piezoelectric crystal apparatus



2 Sheets-Sheet 2 Filed April 5, 1946 m M M w S m m 6 2 6420 WMQWMW M 9999 TEMPERATURE /N DEGREES CENT/GRADE m M m m w T w M 64 64208 nmmnwmmmwmwww TEMPERATURE IN DEGREES CENT/GRADE lA/l/fA/TOR W P. MASON Patented Feb. 1, 1949 UNITED STATES PATENT OFFICIE PIEZOELECTRIC CRYSTAL APPARATUS Warren P. Mason, West Orange, N. J., assignor to Bell Telephone Laboratories, Incorporated, New York, N. Y., a corporation of New York Application April 5, 1946, Serial No. 659,679

13 Claims. 1

This invention relates to piezoelectric crystal apparatus and particularly to synthetic piezoelectric crystal elements comprising sodium chlorate. Such sodium chlorate crystal elements may be used as circuit elements in oscillation generator systems, filter systems, temperature control systems, and in electromechanical systems generally.

One of the objects of this invention is to provide advantageous orientations and modes of motion in piezoelectric crystal elements cut from crystalline sodium chlorate.

Another object of this invention is to take advantage of the low cost, ease of procurement and other advantages of synthetic sodium chlorate crystals.

Another object of this invention is to provide sodium chlorate crystal elements that may possess the maximum value of piezoelectric coupling, and the minimum coupling of the desired mode of motion with undesired modes of motion therein.

Another object of this invention is to provide synthetic piezoelectric crystal elements having a frequency which varies over a wide temperature range in a nearly linear relation with respect to the value of the ambient temperature applied thereto.

Sodium chlorate (NaClOs) is a water soluble crystal substance which has no water of crystallization, which will stand a high temperature, and which crystallizes in the cubic tetrahedral class. As a consequence of its symmetry, there are three elastic constants, one piezoelectric constant and one dielectric constant. The dielectric and piezoelectric constants increase with increase in temperature. As the crystal approaches its melting point, the resistivity and the piezoelectric response are reduced, and the material becomes ionized.

X-ray crystal structure studies show that sodium chlorate has four molecules per unit cell. Each molecule consists of three oxy ens arranged in the form of an equilateral triangle with a separation of 2.38 A. between oxygen centers. The chlorine is located at a distance of 0.48 A. above the plane of the oxygen atoms in a line through the center of gravity of the oxygens. The sodium lies above the chlorine at a distance of 6.12 A.

On account of the large separation of the sodium from the chlorate ion, it is probably the latter which acts as the dipole in the temperature variable part of the dielectric constant. Experimental results for the dielectric constant show that there is a component of the polarization which is practically independent of the temperature and another component which increases With temperature and becomes large as the melting point of the substance is approached. This is presumably due either to an actual orientation of the chlorate dipoles as they become unfrozen at the higher temperatures, or due to an apex reversal of the position of the chlorine in the molecule. Piezoelectric measurements show that the piezoelectric stress due to an applied electric field is directly proportional to the temperature variable component of the polarization and hence it is the change in orientation of the dipoles which causes the distortion of the crystal lattice and hence the piezoelectric effect.

Measurements made an sodium bromate crystal salt show that the temperature-independent component of the polarization for the dielectric constant is larger than that for sodium chlorate, indicating that the polarizability of the bromine is larger than that for chlorine. For equal temperature separations from the Curie point, which is close to the melting point, the temperature variable portion of the polarization is nearly the same size as that for sodium chlorate, indicating that the effective dipole moment is nearly the same for both sodium chlorate and sodium bromate. Piezoelectric measurements show that a given dipole polarization produces over twice as much lattice distortion and hence piezoelectric effect for sodium bromate crystals as for sodium chlorate crystals. Crystal elements comprising sodium bromate are disclosed and claimed in my copending application Serial No. 659,680, filed April 5, 1946.

Crystal elements of suitable orientation cut from crystalline sodium chlorate may be excited in different modes of motion such as the longitudinal length or the longitudinal width modes of motion, or the face shear mode of motion controlled mainly by the major face length and width dimensions. Also, lower frequency flexural modes of motion of either the width bending fiexure type or the thickness bending flexure type may be obtained. These various modes of motion are similar in the general form of their motion to those of similar or corresponding names that are already known in connection with other crystalline substances such as quartz, Rochelle salt and ammonium dihydrogen phosphate crystals.

It is useful to have available synthetic type piezoelectric crystal elements having a resonant frequency which varies in substantially linear relation with respect to temperature. In accordance with this invention, such crystal elements .may be provided, and for this purpose, the cuts may be for example, X-cut, Y-cut and Z-cut crys-' tal plates operating in the major face shear mode of motion and-also iii-degree Y-cut, 45-degr-ee Y-cut and 45-degree Z-cut crystal plates operating in the longitudinal mode of motion.

Such crystal elements having a resonant frequency which varies nearly linearly with respect to temperature change may be utilized as a sensitive thermometer, thermostat or as a thermal regulator that may be continuously regulated. The crystal element may be used for holding the temperature of an enclosure very closely at one temperature, or the control temperature ma be continuously varied by suitable means. The crystal elements may be taken over a very wide temperature range, and have the property that the resonant frequency thereof changes quite uniformly with temperature change, and will hold their frequency quite accurately over such temperature ranges. Either the face shear mode type or the longitudinal mode type of crystal element maybe conveniently utilized for such temperature control units.

For a clearer understanding of the nature of this invention and the additional advantages, features and objects thereof, reference is made to the following description taken in connection with the accompanying drawings, in which like reference characters represent like or similar parts and in which Fig. l is a perspective view illustrating the form and growth habit in which a tetrahedral crystal of sodium chlorate may crystallize, and also illustrating the relation of the surfaces of the mother crystalline substance with respect to the mutually perpendicular X, Y and Z axes and.

the crystallographic a, b and c axes;

Fig. 2 is a perspective view. illustrating O-degree X-cut, Y-cut and Z-cut face shear mode crystal plates, which may be cut from the sodium chlorate mother crystal as illustrated in Fig. 1;

Fig. 3 is a perspective view illustrating 45-degree X-cut, Y-cut and Z-cut longitudinal mode crystal plates, which may be cut from the mother crystal illustrated in Fig. l or from the corresponding X-cut, Y-cut and Z-cut plates illustratedin Fig.2;

Fig. 4 is a graph illustrating the relation between the frequency and the temperature, for X-cut, Y-cut and Z-cut face shear mode sodium chlorate crystal elements as illustrated in Fig. 2;

Fig. 5 is a graph illustrating the relation between the frequency and the temperaturafor 45- degree X-cut, 45-degree Y-cut and 45-deg1ee Z-cut length longitudinal mode sodium chlorate crystal elements as illustrated in Fig. 3.

This specification follows the conventional terminology, as applied to piezoelectric crystal substances, which employs a system of three mutually perpendicular X, Y and Z axes as reference axes for defining the angular orientation of a crystal element. As used in this specification and as shown in the drawing, the Z axis corresponds to the c axis, the Y axis corresponds to the b axis, and the X axis corresponds to the c axis. The crystallographic a, b and c axes represent conventional terminology as used by crystallographers.

Referring to the drawing, Fig. 1 illustrates the general form and growth habit in which sodium chlorate may crystallize. The mother crystal l illustrated in Fig. 1 may be grown from a saturated water solution by slowly reducing the temperature and depositing the salt on a prepared seed. The crystal l grows in the cubic tetrahedral form and, in the case of sodium chlorate crystals, the crystal habit assumes a cubic form as illustrated in Fig. l, the principal faces as expressed in conventional terminology being the 001, 010 and 100 planes, and on the cube edges the 110, 101 and 011 planes are sometimes in evidence.

The mother crystal l, as illustrated in Fig. 1, may be grown from any suitable nutrient solution by any suitable crystallizer apparatus or method, the nutrient solution used for growing the crystal 5 being prepared from any suitable chemical sub stances and the crystal 9 being grown from such nutrient solution in any suitable manner to obtain a mother crystal l of a large size and shape that may be suitable for cutting therefrom piezoelectric crystal elements in accordance with this invention. The mother crystal 9, from which the crystal elements are to be out, is relatively easy to grow in shapes and sizes that are suitable for cutting useful crystal plates or elements therefrom. Such mother crystals 8 may be conveniently grown to sizes around 2 inches or more for the X, Y and Z dimensions or of any size sufiicient to suit the desired size for the piezoelectric circuit elements that are to be out therefrom. It will be understood that the mother crystal I may be grown to size by any suitable crystallizer apparatus such as for example, by a rocking tank type crystallizer or by a reciprocating rotary gyrator type crystallizer.

Crystals 1 comprising sodium chlorate have no water of crystallization and hence no vapor pressure, and accordingly, plates cut therefrom may be put in an evacuated container without change, and may be held in temperatures as high as 200 C. or more. At a temperature #0011- siderably higher than about 240 0., surface decomposition and eventual melting occurs.

Tetrahedral crystals 1 comprising sodium chlorate are characterized by having two interchangeable crystallographic axes b and a, which are disposed at right angles with respect to each other, and a third crystallographic axis c which makes an angle of degrees with respect to the other two crystallographic axes b and a. In dealing with the axes and the properties of such a crystal l, it is convenient to use the mutually perpendicular system of X, Y and Z coordinates. Accordingly, as illustrated in Fig. 1, the method chosen for relating the conventional right-angled X, Y and Z system of axes to the a, b and c system of crystallographic axes of the crystallographer, is to make the Z axis coincide with the c axis and the Y axis coincide with the b or c axis, and to have the X axis coincide" with the a or b crystallographic axis.

Fig. 2 is a perspective view illustrating sodium chlorate X-cut, Y-cut and Z-cut crystal elements 5, 8 and i respectively, cut from a suitable mother crystal i such as that shown in Fig. l. The crystal elements 5, 6 and l as shown in Fig. 2 may be made into the form of plates of substantially rectangular parallelepiped shape having a length dimension L, a breadth or width dimension W, and a thickness or thin dimension T, the directions of the length, width and thickness dimensions L, W and T being mutually perpendicular, and the thin or thickness dimension T being measured between the opposite parallel major or electrode faces of the crystal elements 5, 6 and l. The length dimension L and the width dimension W of the crystal elements 5, 6

and I may be made of values to suit the desired face shear mode frequency thereof. The thickness or thin dimension T may be made of a value to suit the impedance of the system in which the crystal elements 5, 6 and I may be utilized as a circuit element; and also it may be made of a suitable value to avoid nearly spurious modes of motion which, by proper dimensioning of the thickness dimension T relative to the larger length and width dimensions L and W, may be placed in a location that is relatively remote from the desired face shear mode of motion controlled by the length and width dimensions L and W.

Suitable conductive electrodes 3 and 4 may be provided adjacent the two opposite major or electrode faces of the crystal elements 5, 6 and 1 in order to apply electric field excitation thereto. The electrodes 3 and 4 when formed integral with the faces of the crystal elements 5, 6 and I may consist of gold, platinum, silver, aluminum or other suitable conductive mate-rial deposited upon the surfaces of the crystal elements 5, 6 and l by evaporation in vacuum or by other suitable process. Accordingly, it will be understood that the crystal elements 5, B and I may be provided with conductive electrodes or coatings 3 and 4 on their faces of any suitable composition, shape, and arrangement, such as those known for the face shear mode of motion in connection with Rochelle salt or quartz crystals for example; and that they may be nodally mounted and electrically connected by any suitable means such as for example, by a pair of opposite pressure-type clamping pins or conductive supporting spring wires 2 which may be securely cemented by aspot of conductive cement 2a to the tive coatings 3 and 4 deposited on the major faces of the crystal elements 5, as already known in connection with Rochelle salt and other crystals having a similar or corresponding face shear mode of motion. The support wires 2 are individually connected to the electrodes 3 and 4 which are disposed adjacent the opposite major faces of the crystal elements 5, 6 and l and provide an electric field in the direction of the thickness dimension T of the crystal elements 5, 6 and 1, thereby producing a useful face shear mode of motion in the plane of the length and width dimensions L and W of the crystal elements 5, 6 and I.

The face shear mode crystal elements 5, 6 and l of Fig. 2 are three differently oriented crystal elements of X-cut, Y-cut and Z-cut orientations respectively, the frequency of which results from a face shear motion which is controlled in frequency mainly by the major face length and width dimensions L and W. As illustrated in Fig. 2, the major faces of the crystal elements 5, G and 1 are disposed perpendicular or nearly perpendicular with respect to one of the three mutually perpendicular X, Y and Z axes, and the opposite edges of such major faces are disposed parallel or nearly parallel with respect to two of the X, Y and Z axes, the length and width dimensions L and W accordingly being disposed at an angle of zero or nearly zero degrees with respect to two of the X, Y and Z axe-s. motion in the X-cut, Y-cu-t and Z-cut crystal elements 5, 6 and 1 of Fig. 2 is a shear mode of motion controlled by the piezoelectric constants (114, (125 and dse respectively which represent conventional terminology for expressing the relation between the applied field direction and the resulting stress or type of motion. These three piezoelectric constants are of equal value in so- The dium chlorate crystals, and consequently any of the X-cut, Y-cut and Z-cut crystal elements 5, 6 and l of Fig. 2 maybe piezoelectrically driven with equal strength and equal characteristics.

As illustrated in Fig. 2, the X-cut crystal element 5 may have square or rectangular-shaped major faces which are disposed perpendicular or nearly perpendicular with respect to the X axis and which have edges disposed parallel or nearly parallel to the Y and Z axes in order to obtain the desired face shear mode of motion therein free from coupling to longitudinal modes of motion. Similarly, the Y-cut crystal element 6 of Fig. 2 may have its square or rectangular major faces disposed penpendicular or nearly perpendicular to the Y axis and its opposite edges parallel or nearly parallel to the X or Z axes. Similarly, the Z-cut crystal element l of Fig. 2 may have its square or rectangular major faces disposed perpendicular to the Z axis and its edges parallel or nearly parallel to the X and Y axes. In all three of the crystal elements 5, 6 and l of Fig. 2 where the peripheral edges are disposed at a substantially zero angle with respect to two of the three mutually perpendicular X, Y and Z axes, the face shear motion is substantially free from coupling to longitudinal modes therein and has a resonant frequency which is nearly linear with respect to temperature. The frequency constants for the first or fundamental face shear mode of motion of each of the sodium chlorate X-cut, Y-cut and Z-cut crystal elements 5, 6 and 1 respectively of Fig. 2 is of the order of 109 kilocycles per second per centimeter of the length or Width dimension L and W at a temperature of about 25 C., and varies uniformly and nearly linearly with temperature change, as illustrated by the curve in Fig. 4.

While the face shear mode crystal elements 5, 6 and l of Fig. 2 are shown as having substantially square-shaped major faces, they may be cut in elongated rectangular form with small or selected dimensional ratios of width W to length L or of length L to width W, and they may be adapted to vibrate either simultaneously or independently in the first and second shear face modes of motion controlled by the width W and length L dimensions of the crystal element by means as disclosed for example in my United States Patent 2,309,467, dated January 26, 1943.

Fig. 4 is a graph illustrating. an example of the variation in the resonant frequency constant with varying temperatures from about +20 to +250 (3., in fundamental face shear mode crystal elements 5, 6 and I of the X-cut, Y-cut and Z-cut orientations as illustrated in Fig. 2. As shown by the curve in Fig. 4, the frequency constant for the fundamental face shear mode of motion in any of the X-cut, Y-cut and Z-cut crystal elements 5, B and I of Fig. 2 has a value at about 20 C. of about 109 kilocycles per second per centimeter of the length or width dimensions 1'.- and W, and as the temperature is increased, the

I value of the frequency constant decreases uniformly and nearly linearly with respect to temperature change, giving a decrease in frequency constant of about 14 kilocycles per second over the temperature range from about +20 to +250 C., as shown by the curve in Fig. 4.

As an illustrative example from the curve of Fig. 4, an X-cut, a Y-cut or a Z-cut crystal element 5, 6 or I of Fig. 2 having a width dimension W of 1 centimeter and a length dimension L of 1 centimeter will have a frequency for its fundamental face shear mode of motion of about 109 kilocycles. per: second at about C- and of about 95 kilocycles per second at +250 (3., and an intermediate. value between +20 and +250 C as given by the curve ofFig. 4. Similar crystal elements 5, 8 and "l constructed. of other dimensions will have a corresponding frequency which varies inyersely'as the values of the major face width and: length dimensions W and L.

Fig. 3' is a perspective View illustrating three difierently oriented face longitudinal mode crystal elements 8, 9 and H] which may be cut by any suitable methods from a mother crystal I such as that illustrated in Fig. 1, and which may be made into elongated crystal plates of substantially rectangular parallelepiped shape having a relatively large length dimension L, a smaller width dimension W, and a small thickness or thin dimension T which extends between the two opposite major faces of the crystal plates 8, 9 and 10. By proper dimensioning of the thickness dimension T relative to the relatively much larger width and length dimensions W and L, spurious resonances may be placed in a location that is relatively remote from the desired main face mode of motion which in the case of the crystal plates 8, 9 and ID of Fig. 3 is a longitudinal mode of motion.

Suitable conductive electrodes such as the crystal electrodes 3 and 4 may be placed adjacent and formed integral with the opposite major faces of the crystal plates 8, 9 and H3 in order to apply electric field excitation thereto in the di rection of the thickness dimension T thereof. The crystal electrodes 3 and 4 may partially or wholly cover the opposite major faces of the crystal plates 8, 9 and I0, and when formed integral with such faces may consist of gold, platinum, silver, aluminum or other suitable conductive material deposited by evaporation in vacuum, spraying, painting, or by other suitable process.

The 45-degree X-cut, the 45-degree Y-cut and the 45-degree Z-cut crystal elements 8, 9 and I8 respectively of Fig. 3 may be cut from the crystal plates 5, 6 and 1 respectively of Fig. 2, or they may be cut separately from the mother crystal I of Fig. 1. The 45-degree X-cut crystal element 8 as illustrated in Fig. 3 has its opposite major faces disposed perpendicular or nearly perpendicular to the X axis and has its length and width dimensions L and W inclined at an angle of 45 or nearly 45 degrees with respect to the Y and Z axes. Similarly, the 45-degree Y-cut crystal element 9 and the 45-degree Z-cut crystal element IO as illustrated in Fig. 3 have their major faces disposed perpendicular or nearly perpendicular to the Y and Z axes respectively, and have the lengthwise dimension L thereof inclined at an angle of 45 degrees or nearly 45 degrees with respect to the other two of the three mutually perpendicular X, Y and Z axes. The dimensional ratio of the widthdimension W with respect to the length dimension L of the crystal elements 8, 9 and [8 may be of any suitable value such as below 0.7 or around 0.5 or less for example. A feature of interest is that at the bisecting angle of 45 degrees, the crystal elements 8, 9 and I0 illustrated in Fig. 3 have for the longi: tudinal mode of motion, the maximum value for the piezoelectric constants c111, 121 and (131, the maximum value of longitudinal motion, the minimum or zero value of coupling with the face shear mode of motion therein, and a uniform and nearly linear variation in the longitudinal mode frequency with temperature changejas illustrated in Fig. 5.

While the 45-degree angle asv illustratedin Fig. 3 is of special interest, it will be understood that the longitudinal mode crystal elements 8, 8V and 18 may be rotated in effect about their thickness dimension '1 to a position at either side of and other than at the 45-degree bisecting angular position that is particularly illustrated in Fig. 3. And while the longitudinal mode. of motion along the. length dimension L is of special interest, it will be understood that the crystal elements 8, 9 and ID of Fig. 3 may be operated in the longitudinal mode of motion along the width dimension W by the same electrodes 3 and 4; or they may beoperated simultaneously in the length L and width W longitudinal modes of motion by electrode means as disclosed in my United States Patent 2,292,885, dated August 11, 1942; or they may be operated alone or simultaneously in the length L longitudinal mode of motion and in the width W flexural mode of motion by means as disclosed in my United States Patent 2,292,886, dated August 11, 1942.

The dimensional ratio of the Width dimension W with respect to the length dimension L of the crystal elements 8, 9' and It may be made of any suitable value in the region less than 0.7 for example, and as particularly described herein is less than 0.5 for longitudinal length L mode crystal elements. The smaller values of dimensional ratios of the width W with respect to the length L, as of the order of 0.5 more or less, have the effect of spacing the width W mode of motion therein at a frequency which is remote from the fundamental. longitudinal mode of motion along the length. dimension L.

the crystal elements 8, 9 and [8 are oper ed in the fundamental longitudinal mode of motion along the length dimension L thereof, the nodalline occurs at the center of and transverse to the length dimension L of the crystal element and is about midway between the opposite small ends thereof, and the crystal element 8, 9 or [8 may be there nodally mounted and electrically connected by any suitable means such as by one or more pairs of coaxial sprin wires 2 which may be secured or cemented by a spot of conductive cement 2a to the metallic coatin s 3 and 4 in the nodal region 2a of the crystal elements 8, 9 and l 0.

While the crystal elements 8, 9 and ii) are particularly described herein as being operated in the fundamental longitudinal mode of motion along the length dimension L, it will be understood that they may be operated in any even or odd order harmonic thereof by means of a plurality of pairs of opposite interconnected electrodes spaced along the length dimension L thereof in a manner known in connection with longitudinal mode quartz crystal elements.

The cuts of special interest illustrated in Fig. 3 are the 45-degree X-cut, the 45-degree Y-cut and the 45-degree Z-cut crystal elements 8, 9 and I9 respectively as illustrated in Fig. 3, which are adapted to vibrate in the longitudinal mode of motion along the lengthwise dimension L of the major faces thereof. These three cuts have similar characteristics and they are the orientations linear relation with respect to the temperature change over a wide range, a feature which is of interest in connection with temperature control uses. It will be noted that the 45-degree X-cut, the 45-degree Y-cut and the 45-degree Z-cut crystal elements 8, 9 and II] respectively have similar characteristics, and that their frequency constants expressed in kilocycles per secondper centimeter of the length dimension L in a temperature range from about +25 C. to +240 C'., are roughly from 182 to 160 according to the value of the temperature. 1

As an illustrative example for a 45-degree Z-cut sodium chlorate crystal element I having a length dimension L equal to about 20.38 millimeters, a width dimension W of about 2.71 millimeters and a thickness dimension T of about 1.01 millimeters, the frequency constant expressed in kilocycles per second per centimeter of the length dimension L is about 181.8 at +28 0., about 180.9 at +40 C., about 179.3 at +75 C. and decreases uniformly to about 160.2 at +240 C., as given in the followin table which also gives corresponding values for two other Z-cut crystal elements where the length dimension L is disposed at an angle of 0 degrees and also at an angle of 22 degrees with respect to the X axis:

TABLE Measured properties of sodium chlorate Z-Cut; L=22.5 Z-Cut; L=45 7mm: Temperature in ia?? L=IE8IBHH L=29.90 mm Degrees C. W=2I69 W=2'71 mm W 6.02 mm T=l.00 mm. T=1.0l mm T494 mm Kc.-cm. Kc.cm. Kc.cm.

19s. 2 131. 8 10s. 6 192. 2 180. 9 10s. 3 190. 2 179. 3 108.2 187. 2 177. 2 106. 2 183. 4 17s. 104. 2 182. 3 172. 5 103. s 131. 3 171. 3 103. 1 170. 3 102. 5 178.6 169. 2 102. 0 177. 5 168. 3 101. 2 17s. 1 167. 1 100. 4 175. 1 166. 2 09.9 173. 1 164. 5 e9. 1 172. 2 163. 3 9s. 3 170. a 161. 3 97. 2 168. 5 160. 2 9c. 2

Fig. 5 is a graph illustrating an example of the variation in the resonant frequency constant With varying temperatures from about +25 to +240 C., in longitudinal mode elongated crystal elements 8, 9 and ID of the 45-degree X-cut, 45-degree Y-cut and 45-degree Z-cut orientations respectively which are particularly illustrated in Fig. 3. As shown by the curve in Fig. 5, the frequency constant for the fundamental longitudinal length mode of motion in any of the elongated crystal elements 8, 9 and ID of Fig. 3 has at a temperature of about 25 C. a value of about 182 kilocycles per second per centimeter of the length dimension L, and as the temperature is increased, the value of the frequency constant decreases uniformly and nearly linearly with respect to temperature change, giving a decrease in frequency constant of about 22 kilocycles per second over the temperature range from about +25 to +240 0., as shown by the curve in Fig. 5. The frequency of the longitudinal mode of motion along the length dimension varies inversely as the value of the temperature, and also inversely as the value of the length dimension L.

Although this invention has been described and illustrated in relation to specific arrangements, it is to be understood that it is capable of application in other organizations and is therefore not to be limited to the particular embodiments disclosed.

What is claimed is:

l. Piezoelectric crystal apparatus comprising a piezoelectric sodium chlorate crystal plate having its substantially rectangular-shaped major faces disposed substantially perpendicular to one of the three mutually perpendicular Y and Z axes, the opposite edges of said major faces being disposed at one of the angles of substantially 0 and degrees with respect to one of the other two of said three mutually perpendicular X, Y and Z axes, and means comprising electrodes disposed adjacent said major faces for operating said crystal plate in a face mode of motion at a frequency which varies in substantially uniform linear relation with respect to the value of ambient temperature applied thereto.

2. Piezoelectric crystal apparatus comprising a sodium chlorate crystal element adapted for vibration in the face shear mode of motion alon its substantially rectangular major faces at a frequency which varies uniformly over a substantial temperature range in accordance With the value of the temperature thereof, said major faces being disposed substantially perpendicular to the X axis, and the edges of said major faces being dispose-d substantially parallel to the Y and Z axes and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said face shear mode of motion at said frequency in accordance with said temperature value.

3. Piezoelectric crystal apparatus comprising a sodium chlorate crystal element adapted for vibration in the face shear mode of motion along its substantially square major faces at a frequency which varies uniformly over a substantial temperature range in accordance with the value of the temperature thereof, said major faces being disposed substantially perpendicular to the -X axis, and the edges of said major faces being disposed substantially parallel to the Y and Z axes, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said face shear mode of motion at said frequency in accordance with said temperature value.

4. Piezoelectric crystal apparatus comprising a sodium chlorate crystal element adapted for vi-, bration in the face shear mode of motion along its substantially rectangular major faces at a frequency which varies uniforml over a substantial temperature range in accordance with the value of the temperature thereof, said major faces being disposed substantially perpendicular to the Y axis, and the edges of said major faces being disposed substantially parallel to the X and Z axes, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said face shear mode of motion at said frequency in accordance with said temperature value.

5. Piezoelectric crystal apparatus comprising a sodium chlorate crystal element adapted for vibation in the face shear mode of motion along its substantially square major faces a frequency Which varies uniformly over a substantial temperature range in accordance with the value of the temperature thereof, said major faces being disposed substantially perpendicular to the Y axis, and the edges of said major faces being disposed substantially parallel to the X and Z axes, and means comprising electrodes disposed adjabration in the face shear mode of motion along its substantially rectangular major faces at a frequency which varies uniformly over a substantial temperature range in accordance with the value of the temperature thereof, said major faces being disposed substantially perpendicular to the Z axis, and the edges of said major faces being disposed substantially parallel to the Y and X axes,.and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said face shear mode of motion at said frequency in accordance with said temperature value.

7. Piezoelectric'crystal apparatus comprising a sodium chlorate crystal element adapted for vibration in the face shear mode of motion along its substantially square major faces at a frequency which varies uniformly over a substantial temperature range in accordance with the value of the temperature thereof, said major faces being disposed substantially perpendicular to the Z axis, and the edges of said major faces being disposed substantially parallel to the Y and X axes, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said face shear mode of motion at said frequency in accordance with said temperature value.

8. Piezoelectric crystal apparatus comprising a sodium chlorate crystal element adapted for vibration in the face shear mode of motion along its substantially rectangular major faces, said major faces being disposed substantially perpendicular with respect to one of the three mutually perpendicular X, Y and Z axes, the length and width dimensions of said major faces being disposed substantially parallel with respect to one of the other two of said three mutually perpendicular X, Y and Z axes, said length and width dimensions having values corresponding to the value of the frequency for said face shear mode of motion, said length and width dimensions expressed in centimeters being one of the values substantially from 110 to 95 divided by said value of said frequency expressed in kilocycles per second, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said face shear mode of motion at said frequency, said frequency being a value which varies uniformly in accordance with the value of the ambient temperature applied to said crystal element and said frequency corresponding to a value substantially as given by the curve in Fig. 4 at a point thereon corresponding to the value of said temperature.

9. Piezoelectric crystal apparatus comprising an elongated sodium chlorate crystal element adapted for vibration in the longitudinal mode of motion along the lengthwise dimension of its substantially rectangular major faces, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said lengthwise mode of motion at a frequency which varies uniformly over a substantial temperature range in accordance with the value of the temperature of said crystal element, said major faces being disposed substantially perpendicular to the X axis, and said lengthwise dimension being inclined at an angle of substan- 12 tially 45 degrees with respect 'to the Y and Z axes.

10. Piezoelectric crystal-apparatus comprising an elongated sodium chlorate crystal element adapted for vibration in the longitudinal mode of motion along the lengthwise dimension of its substantially rectangular major faces, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said lengthwise mode of motion at a frequency which varies uniformly over a substantial temperature range in accordance with the value of the temperature of said crystal element, said major faces being disposed substantially perpendicular to the Y axis, and said lengthwise dimension being inclined at an angle of substantially degrees with respect to the X and Z axes.

l1. Piezoelectric crystal apparatus comprising an elongated sodium chlorate crystal element adapted for vibration in the longitudinal mode of motion along the lengthwise dimension of its substantially rectangular major faces, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said lengthwise mode of motion at a frequency which varies uniformly over a substantial temperature range in accordance with the value of the temperature of said crystal element, said major faces being disposed substantially perpendicular to the Z axis, and said lengthwise dimension being inclined at an angle of substantially 45 degrees with respect to the Y and X axes.

12. Piezoelectric crystal apparatus comprising a sodium chlorate crystal element adapted for longitudinal motion along the length dimension of its substantially rectangular major faces, said major faces being disposed substantially perpen dicular with respect to one of the three mutu- 0 ally perpendicular X, Y and Z axes, said length dimension being disposed at an angle of substantially 45 degrees with respect to the other two of said three mutually perpendicular X, Y and Z axes, the width dimension of said major faces being substantially less than said length dimension thereof, said length dimensionhaving a value corresponding to the value of the frequency for said longitudinal mode of motion, said length dimension expressed in centimeters being one of the values substantially from 182 to divided by said value of said frequencyexpressed in kilocycles per second, and means comprising electrodes disposed adjacent said major faces for operating said crystal element in said longitudinal mode of motion at said frequency, said frequency being a value which varies uniformly in accordance with the value of the ambient temperature applied to said crystal element and said frequency corresponding to a value'substantially as given by the curve in Fig. 5 at a point thereon corresponding to the value of said temperature.

13. Piezoelectric crystal apparatus comprising a piezoelectric sodium chlorate crystal element having substantially rectangular-shaped major faces, said major faces being disposed substantiallyperpendicular to one of the three mutually perpendicular X, Y and Zaxes, the lengthwise dimension and longest edges of said major faces being inclined at an orientation angleof substantially 45 degrees with respect to'the other two of said three mutually perpendicular X, Y and Z axes, and means comprising electrodes disposed adjacent said major faces for operating said crystal element 'in a-ilongitudinal mode of motion at a frequency dependent -.upon said 9,460,708 13 14 lengthwise dimension and having a value which REFERENCES CITED varies uniformly with respect to the value of the temperature of said crystal element, said orien- The following references are of record in the tation angle being a value corresponding to the file Of this P maximum value of piezoelectric coupling for said 5 UNITED STATES PATENTS longitudinal mode of motion, and corresponding to a substantially zero value for the coupling of Number Name Date said longitudinal mode of motion to the face 2 105,01 Williams Jan, 11, 1933 shear mode of motion along said major fages of 2 292 33 Mason 11, 1942 said crystal element, the ratio of the wid h di- 10 cmension and shortest edges of said major faces OTHER REFERENCES With p t 60 said lengthwise dimension and Bruzan, Electrical Communications, vol. 23, longest edges thereof being a value less than 0.7, p, 4454159, D ember 1946,

said lengthwise dimension expressed in centime- Mason, Physical i 1, 70, 529-537,

ters being substantially one of the values from 15 October 1, 1946. 182 to 160 divided by said frequency expressed in kilocycles per second.

WARREN P. MASON. 

